SU(2)^2xU(1)-invariant G_2-instantons on the AC limit of the C7 family

TL;DR

This paper constructs a family of invariant G_2-instantons on a specific asymptotically conical G_2 manifold using a dynamical systems approach, revealing new solutions with bounded curvature.

Contribution

It introduces a novel method for constructing invariant G_2-instantons on the AC limit of the C7 family, expanding the understanding of gauge theory on special holonomy manifolds.

Findings

Established a 1-parameter family of instantons with bounded curvature

Used perturbation techniques of abelian and cone solutions

Demonstrated the existence of invariant instantons on the AC limit

Abstract

We construct SU(2)^2xU(1)-invariant G_2-instantons on the asymptotically conical limit of the C7 family of G_2-metrics. The construction uses a dynamical systems approach involving perturbations of an abelian solution and a solution on the G_2-cone. From this we obtain a 1-parameter family of invariant instantons with gauge group SU(2) and bounded curvature.